Assume that fk is the probability of getting a face k in a single throw of the die, k=1,2,3..,6.
Naturally, for k=7, fk is the probability of getting a 7 in a single throw of a six faced die, which is impossible and hence for k=7, fk=0.
For k=1.5, fk is the probability of getting a 1.5 (i.e. a fractional face) in a single throw of a six faced die, which is impossible and hence for k=1.5, fk=0.
* Question 1: For the six-sided fair die, what is fk if k= 7? k= 1.5?...
For the fair 6-sided die, what is F(3)? F(7)? F(1.5)?
In this experiment, both a fair four-sided die and a fair six-sided die are rolled (these dice both have the numbers most people would expect on them). Let Z be a random variable that represents the absolute value of their difference. For instance, if a 4 and a 1 are rolled, the corresponding value of Z is 3. (a) What is the pmf of Z? (b) Draw a graph of the cdf of Z
Consider a fair six-sided die. (a) What is its probability mass function? Graph it. It represents the population distribution of outcomes of rolls of a six-sided die (b) How would you describe the population distribution? (c) What is the sampling distribution of x for a six-sided fair die, when its rolled 100 times? Describe it with as much specificity as possible. NOTE: Roll of a die is a discrete variable. Why is it ok to use the Normal distribution to...
1. Suppose a fair six-sided die is tossed, with N being the resulting number on the uppermost face. Given N, a fair coin is tossed independently until N heads are recorded. Let X be the total number of tails recorded. a. What is the pmf of N? (5 pts) b. Given N = 3, what is the distribution of X? (10 pts) c. What is Pr(X = 1)? (10 pts) d. What is E(X)? (10 pts)
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the six-sided die is an even number and B be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions.What is P(A), the probability that the six-sided die is an even number?What is P(B), the probability that the four-sided die is an odd number?What is P(A...
3. A fair coin is tossed, and a fair six-sided die is rolled. What is the probability that the coin come up heads and the die will come up 1 or 2? A. 1/2 B. 1/4 C. 1/6 E. 1/3
1) For a fair six-sided die, determine the following probabilites: A. Getting a 2 and a 6 on two independent die rolls. B. NOT getting a 4 on a single die roll.
1) For a fair six-sided die, determine the following probabilites: A. Getting a 2 and a 6 on two independent die rolls. B. NOT getting a 4 on a single die roll.
in a game, you toss a fair coin and a fair six sided die. if you toss a heads on the coin and roll either a 3 or a 6 on the die, you win $30. otherwise, you lose $6. what is the expected profit of one round of this game
1. A casino wants to see if a six-sided die is fair. They perform an experiment in which they roll the die 100 times and count the number of times the result is a 3. (a) Is this a one or two-sided test? Explain your answer in a complete sentence. (b) Set up the hypotheses for this test both in words and in terms the parameter p which denotes the theoretical probability for getting a roll of the die giving...